An M/M/1 queue with a general bulk service rule Academic Article uri icon


  • A model of an M/M/1 bulk queue with service rates dependent on the batch size is developed. The operational policy is to commence service when at least L customers are available with a maximum batch size of K. Arriving customers are not allowed to join in-process service. The solution procedure utilizes the matrix geometric methodology and reduces to obtaining the inverse of a square matrix of dimension K plus 1 minus L. For the case where the service rates are not batch size dependent, the limiting probabilities can be written in closed form. A numerical example illustrates the variability of the system cost as a function of the minimum batch service size L.

published proceedings

  • Naval Research Logistics Quarterly

author list (cited authors)

  • Curry, G. L., & Feldman, R. M.

citation count

  • 15

complete list of authors

  • Curry, Guy L||Feldman, Richard M

publication date

  • November 1985